Reflecting a Shape in the Y-Axis Using Cartesian Coordinates
(KS3, Year 7)
A shape can be reflected in the y-axis. If point on a shape is reflected in the y-axis, the y-coordinate stays the same, but the x-coordinate changes sign (becomes negative if it is positive and vice versa). The image below shows a point on a shape being reflected in the y-axis:

reflect a shape in y-axis_cartesian_coordinates
  • The point A has Cartesian coordinates (3, 4).
  • The reflected point A' has Cartesian coordinates (−3, 4). The y-coordinate is still 4, but the x-coordinate has changed from 3 to −3.

How to Reflect a Shape in the Y-Axis Using Cartesian Coordinates

Reflecting a shape in the y-axis using Cartesian coordinates is easy.

Question

Reflect the shape below in the y-axis.
reflect a shape in y-axis_cartesian_coordinates_example

Step-by-Step:

1

Find the Cartesian coordinates of each point on the shape. Write the x-coordinates and y-coordinates of each point.
Point x-coordinate y-coordinate
A −3 2
B −2 5
C −1 2

2

Find the Cartesian coordinates of the reflected points. Keep the y-coordinate the same, but change the sign of the x-coordinate.
Point x-coordinate y-coordinate Point x-coordinate y-coordinate
A −3 2 A' 3 2
B −2 5 B' 2 5
C −1 2 C' 1 2

3

Plot the reflected points and draw in the shape.

Answer:

We have reflected the shape in the y-axis.

reflect a shape in y-axis_cartesian_coordinates_answer

A Formula to Reflect a Point in the Y-Axis Using Cartesian Coordinates

In general, we write Cartesian coordinates as: cartesian_coordinate_point x is the x-coordinate. y is the y-coordinate. x and y can taken any number. The reflected point has Cartesian coordinates:

cartesian coordinate point reflected in y-axis The image below shows a general Cartesian coordinate being reflected in the y-axis:

reflect a shape in y-axis_cartesian_coordinates_formula

Lesson Slides

The slider below shows another real example of how to reflect a shape in the y-axis using Cartesian coordinates. Open the slider in a new tab

What Is a Reflection?

A reflection flips a shape so that it becomes a mirror image of itself. A reflection is a type of transformation.
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This page was written by Stephen Clarke.